gibson:teaching:fall-2016:math753:finitediff

The main things to know here are a few formulae for approximating derivatives using finite differences:

Given a set of evenly space gridpoints , where , and a function evaluated at the gridpoints , we can approximate the first derivative of at the gridpoints several ways

**One-sided finite differencing for the first derivative**, rightwards

**One-sided finite differencing for the first derivative**, leftwards

**Centered finite differencing for the first derivative**

In practice you use the fraction on the right-hand-side as an approximation of the derivative, knowing that there is an or error in the approximation.

To approximate the second derivative , we use the

**Centered finite differencing for the second derivative**

There are many, many other finite-difference formulae, for higher-order derivatives, higher-order accuracy, and different choices of which gridpoint values enter into the formula. As a starting point, see the following

Further reading

- Finite Difference (wikipedia)
- Finite Differences lecture (Mohamed Iskandarani, University of Miami)

gibson/teaching/fall-2016/math753/finitediff.txt · Last modified: 2016/12/12 18:49 by gibson